The Telescoping series reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Telescoping series

In mathematics, telescoping series is an informal expression referring to a series whose sum can be found by exploiting the circumstance that nearly every term cancels with a succeeding or preceding term.

For example, the series

simplifies as

While telescoping is a neat technique, there are pitfalls to watch out for:

is not correct because regrouping of terms is invalid unless the individual terms converge to 0.

This is the "Telescoping series" reference article from the English Wikipedia. All text is available under the terms of the GNU Free Documentation License. See also our Disclaimer.